{"title":"关于无限树上Dirichlet问题的几点注记","authors":"Nikolaos Chalmoukis, Matteo Levi","doi":"10.1515/conop-2019-0002","DOIUrl":null,"url":null,"abstract":"Abstract We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"6 1","pages":"20 - 32"},"PeriodicalIF":0.3000,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2019-0002","citationCount":"7","resultStr":"{\"title\":\"Some remarks on the Dirichlet problem on infinite trees\",\"authors\":\"Nikolaos Chalmoukis, Matteo Levi\",\"doi\":\"10.1515/conop-2019-0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.\",\"PeriodicalId\":53800,\"journal\":{\"name\":\"Concrete Operators\",\"volume\":\"6 1\",\"pages\":\"20 - 32\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/conop-2019-0002\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Concrete Operators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/conop-2019-0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2019-0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some remarks on the Dirichlet problem on infinite trees
Abstract We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.
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